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-   -   Prime Numbers | 4 Aug 2009 (http://www.go4expert.com/contests/prime-numbers-4-aug-2009-t18812/)

 shabbir 4Aug2009 20:09

Prime Numbers | 4 Aug 2009

List a set of prime numbers where the sum total of the complete set is 100.

 rik625 4Aug2009 20:27

Re: Prime Numbers | 4 Aug 2009

The sum of first 9 prime number is 100:

2
3
5
7
11
13
17
19
23

 rik625 4Aug2009 20:28

Re: Prime Numbers | 4 Aug 2009

Well there are other possiblities too..but im just considering the first set n obviously the easier one to figure out... :P

Re: Prime Numbers | 4 Aug 2009

97 and 3

Re: Prime Numbers | 4 Aug 2009

Quote:
 Originally Posted by rik625 (Post 54224) The sum of first 9 prime number is 100: 2 3 5 7 11 13 17 19 23
The first (and smallest) set that I could think of immediately was 97+3.
So, congrats :)

 rik625 4Aug2009 20:39

Re: Prime Numbers | 4 Aug 2009

Thanks saswat :)

 nimesh 4Aug2009 20:44

Re: Prime Numbers | 4 Aug 2009

Listings all possible sets that I could think of :)

03 97
11 89
02 03 05 07 83
02 03 05 11 79
02 03 05 17 73
02 03 05 19 71
02 07 11 13 67
02 07 13 17 61
02 07 11 19 61
02 03 05 07 11 13 59
02 03 05 07 13 17 53
02 03 05 11 13 19 47
03 05 13 17 19 43
02 03 05 13 17 19 41
03 11 13 17 19 37
02 07 11 13 17 19 31
02 03 05 07 11 13 17 19 23
05 07 17 19 23 29
07 11 13 17 23 29

 shabbir 4Aug2009 21:35

Re: Prime Numbers | 4 Aug 2009

Quote:
 Originally Posted by rik625 (Post 54224) The sum of first 9 prime number is 100: 2 3 5 7 11 13 17 19 23
This are the first 9 prime numbers as well which when verifying yesterdays sum hit as 100. So formed this one.

 nimesh 4Aug2009 21:54

Re: Prime Numbers | 4 Aug 2009

Congrats rik

Re: Prime Numbers | 4 Aug 2009

Quote:
 Originally Posted by nimesh (Post 54229) Listings all possible sets that I could think of :) 03 97 11 89 02 03 05 07 83 02 03 05 11 79 02 03 05 17 73 02 03 05 19 71 02 07 11 13 67 02 07 13 17 61 02 07 11 19 61 02 03 05 07 11 13 59 02 03 05 07 13 17 53 02 03 05 11 13 19 47 03 05 13 17 19 43 02 03 05 13 17 19 41 03 11 13 17 19 37 02 07 11 13 17 19 31 02 03 05 07 11 13 17 19 23 05 07 17 19 23 29 07 11 13 17 23 29
OK, now that I have coded my own super-fast generator, I would like to mention that this list is far from complete, the complete list has 233 different sets. The list is :

--> { 3, 97 }
--> { 11, 89 }
--> { 17, 83 }
--> { 29, 71 }
--> { 41, 59 }
--> { 47, 53 }
--> { 2, 19, 79 }
--> { 2, 31, 67 }
--> { 2, 37, 61 }
--> { 3, 5, 13, 79 }
--> { 3, 5, 19, 73 }
--> { 3, 5, 31, 61 }
--> { 3, 7, 11, 79 }
--> { 3, 7, 17, 73 }
--> { 3, 7, 19, 71 }
--> { 3, 7, 23, 67 }
--> { 3, 7, 29, 61 }
--> { 3, 7, 31, 59 }
--> { 3, 7, 37, 53 }
--> { 3, 7, 43, 47 }
--> { 3, 11, 13, 73 }
--> { 3, 11, 19, 67 }
--> { 3, 11, 43, 43 }
--> { 3, 13, 17, 67 }
--> { 3, 13, 23, 61 }
--> { 3, 13, 31, 53 }
--> { 3, 13, 37, 47 }
--> { 3, 13, 41, 43 }
--> { 3, 17, 19, 61 }
--> { 3, 17, 37, 43 }
--> { 3, 19, 31, 47 }
--> { 3, 19, 37, 41 }
--> { 3, 23, 31, 43 }
--> { 3, 23, 37, 37 }
--> { 3, 29, 31, 37 }
--> { 5, 7, 17, 71 }
--> { 5, 7, 29, 59 }
--> { 5, 7, 41, 47 }
--> { 5, 11, 13, 71 }
--> { 5, 11, 17, 67 }
--> { 5, 11, 23, 61 }
--> { 5, 11, 31, 53 }
--> { 5, 11, 37, 47 }
--> { 5, 11, 41, 43 }
--> { 5, 13, 23, 59 }
--> { 5, 13, 29, 53 }
--> { 5, 13, 41, 41 }
--> { 5, 17, 19, 59 }
--> { 5, 17, 31, 47 }
--> { 5, 17, 37, 41 }
--> { 5, 19, 23, 53 }
--> { 5, 19, 29, 47 }
--> { 5, 23, 29, 43 }
--> { 5, 23, 31, 41 }
--> { 7, 11, 23, 59 }
--> { 7, 11, 29, 53 }
--> { 7, 11, 41, 41 }
--> { 7, 13, 19, 61 }
--> { 7, 13, 37, 43 }
--> { 7, 17, 23, 53 }
--> { 7, 17, 29, 47 }
--> { 7, 19, 31, 43 }
--> { 7, 19, 37, 37 }
--> { 7, 23, 29, 41 }
--> { 11, 13, 17, 59 }
--> { 11, 13, 23, 53 }
--> { 11, 13, 29, 47 }
--> { 11, 17, 19, 53 }
--> { 11, 17, 29, 43 }
--> { 11, 17, 31, 41 }
--> { 11, 19, 23, 47 }
--> { 11, 19, 29, 41 }
--> { 11, 23, 29, 37 }
--> { 13, 17, 23, 47 }
--> { 13, 17, 29, 41 }
--> { 13, 19, 31, 37 }
--> { 17, 19, 23, 41 }
--> { 17, 23, 29, 31 }
--> { 19, 23, 29, 29 }
--> { 2, 3, 5, 7, 83 }
--> { 2, 3, 5, 11, 79 }
--> { 2, 3, 5, 17, 73 }
--> { 2, 3, 5, 19, 71 }
--> { 2, 3, 5, 23, 67 }
--> { 2, 3, 5, 29, 61 }
--> { 2, 3, 5, 31, 59 }
--> { 2, 3, 5, 37, 53 }
--> { 2, 3, 5, 43, 47 }
--> { 2, 3, 7, 17, 71 }
--> { 2, 3, 7, 29, 59 }
--> { 2, 3, 7, 41, 47 }
--> { 2, 3, 11, 13, 71 }
--> { 2, 3, 11, 17, 67 }
--> { 2, 3, 11, 23, 61 }
--> { 2, 3, 11, 31, 53 }
--> { 2, 3, 11, 37, 47 }
--> { 2, 3, 11, 41, 43 }
--> { 2, 3, 13, 23, 59 }
--> { 2, 3, 13, 29, 53 }
--> { 2, 3, 13, 41, 41 }
--> { 2, 3, 17, 19, 59 }
--> { 2, 3, 17, 31, 47 }
--> { 2, 3, 17, 37, 41 }
--> { 2, 3, 19, 23, 53 }
--> { 2, 3, 19, 29, 47 }
--> { 2, 3, 23, 29, 43 }
--> { 2, 3, 23, 31, 41 }
--> { 2, 5, 7, 13, 73 }
--> { 2, 5, 7, 19, 67 }
--> { 2, 5, 7, 43, 43 }
--> { 2, 5, 11, 23, 59 }
--> { 2, 5, 11, 29, 53 }
--> { 2, 5, 11, 41, 41 }
--> { 2, 5, 13, 19, 61 }
--> { 2, 5, 13, 37, 43 }
--> { 2, 5, 17, 23, 53 }
--> { 2, 5, 17, 29, 47 }
--> { 2, 5, 19, 31, 43 }
--> { 2, 5, 19, 37, 37 }
--> { 2, 5, 23, 29, 41 }
--> { 2, 7, 11, 13, 67 }
--> { 2, 7, 11, 19, 61 }
--> { 2, 7, 11, 37, 43 }
--> { 2, 7, 13, 17, 61 }
--> { 2, 7, 13, 19, 59 }
--> { 2, 7, 13, 31, 47 }
--> { 2, 7, 13, 37, 41 }
--> { 2, 7, 17, 31, 43 }
--> { 2, 7, 17, 37, 37 }
--> { 2, 7, 19, 29, 43 }
--> { 2, 7, 19, 31, 41 }
--> { 2, 7, 23, 31, 37 }
--> { 2, 7, 29, 31, 31 }
--> { 2, 11, 13, 31, 43 }
--> { 2, 11, 13, 37, 37 }
--> { 2, 11, 17, 23, 47 }
--> { 2, 11, 17, 29, 41 }
--> { 2, 11, 19, 31, 37 }
--> { 2, 13, 17, 31, 37 }
--> { 2, 13, 19, 23, 43 }
--> { 2, 13, 19, 29, 37 }
--> { 2, 13, 23, 31, 31 }
--> { 2, 17, 19, 31, 31 }
--> { 2, 17, 23, 29, 29 }
--> { 3, 5, 7, 11, 13, 61 }
--> { 3, 5, 7, 11, 31, 43 }
--> { 3, 5, 7, 11, 37, 37 }
--> { 3, 5, 7, 13, 19, 53 }
--> { 3, 5, 7, 13, 29, 43 }
--> { 3, 5, 7, 13, 31, 41 }
--> { 3, 5, 7, 17, 31, 37 }
--> { 3, 5, 7, 19, 23, 43 }
--> { 3, 5, 7, 19, 29, 37 }
--> { 3, 5, 7, 23, 31, 31 }
--> { 3, 5, 11, 13, 31, 37 }
--> { 3, 5, 11, 17, 23, 41 }
--> { 3, 5, 11, 19, 31, 31 }
--> { 3, 5, 11, 23, 29, 29 }
--> { 3, 5, 13, 17, 19, 43 }
--> { 3, 5, 13, 17, 31, 31 }
--> { 3, 5, 13, 19, 23, 37 }
--> { 3, 5, 13, 19, 29, 31 }
--> { 3, 7, 11, 13, 19, 47 }
--> { 3, 7, 11, 13, 23, 43 }
--> { 3, 7, 11, 13, 29, 37 }
--> { 3, 7, 11, 17, 19, 43 }
--> { 3, 7, 11, 17, 31, 31 }
--> { 3, 7, 11, 19, 23, 37 }
--> { 3, 7, 11, 19, 29, 31 }
--> { 3, 7, 13, 17, 19, 41 }
--> { 3, 7, 13, 17, 23, 37 }
--> { 3, 7, 13, 17, 29, 31 }
--> { 3, 7, 13, 19, 29, 29 }
--> { 3, 7, 17, 19, 23, 31 }
--> { 3, 11, 13, 17, 19, 37 }
--> { 3, 11, 13, 19, 23, 31 }
--> { 5, 7, 11, 13, 17, 47 }
--> { 5, 7, 11, 13, 23, 41 }
--> { 5, 7, 11, 17, 19, 41 }
--> { 5, 7, 11, 17, 23, 37 }
--> { 5, 7, 11, 17, 29, 31 }
--> { 5, 7, 11, 19, 29, 29 }
--> { 5, 7, 13, 17, 29, 29 }
--> { 5, 7, 17, 19, 23, 29 }
--> { 5, 11, 13, 17, 23, 31 }
--> { 5, 11, 13, 19, 23, 29 }
--> { 5, 13, 17, 19, 23, 23 }
--> { 7, 11, 13, 17, 23, 29 }
--> { 7, 11, 17, 19, 23, 23 }
--> { 2, 3, 5, 7, 11, 13, 59 }
--> { 2, 3, 5, 7, 11, 19, 53 }
--> { 2, 3, 5, 7, 11, 29, 43 }
--> { 2, 3, 5, 7, 11, 31, 41 }
--> { 2, 3, 5, 7, 13, 17, 53 }
--> { 2, 3, 5, 7, 13, 23, 47 }
--> { 2, 3, 5, 7, 13, 29, 41 }
--> { 2, 3, 5, 7, 17, 19, 47 }
--> { 2, 3, 5, 7, 17, 23, 43 }
--> { 2, 3, 5, 7, 17, 29, 37 }
--> { 2, 3, 5, 7, 19, 23, 41 }
--> { 2, 3, 5, 7, 23, 29, 31 }
--> { 2, 3, 5, 11, 13, 19, 47 }
--> { 2, 3, 5, 11, 13, 23, 43 }
--> { 2, 3, 5, 11, 13, 29, 37 }
--> { 2, 3, 5, 11, 17, 19, 43 }
--> { 2, 3, 5, 11, 17, 31, 31 }
--> { 2, 3, 5, 11, 19, 23, 37 }
--> { 2, 3, 5, 11, 19, 29, 31 }
--> { 2, 3, 5, 13, 17, 19, 41 }
--> { 2, 3, 5, 13, 17, 23, 37 }
--> { 2, 3, 5, 13, 17, 29, 31 }
--> { 2, 3, 5, 13, 19, 29, 29 }
--> { 2, 3, 5, 17, 19, 23, 31 }
--> { 2, 3, 7, 11, 13, 17, 47 }
--> { 2, 3, 7, 11, 13, 23, 41 }
--> { 2, 3, 7, 11, 17, 19, 41 }
--> { 2, 3, 7, 11, 17, 23, 37 }
--> { 2, 3, 7, 11, 17, 29, 31 }
--> { 2, 3, 7, 11, 19, 29, 29 }
--> { 2, 3, 7, 13, 17, 29, 29 }
--> { 2, 3, 7, 17, 19, 23, 29 }
--> { 2, 3, 11, 13, 17, 23, 31 }
--> { 2, 3, 11, 13, 19, 23, 29 }
--> { 2, 3, 13, 17, 19, 23, 23 }
--> { 2, 5, 7, 11, 13, 19, 43 }
--> { 2, 5, 7, 11, 13, 31, 31 }
--> { 2, 5, 7, 11, 17, 29, 29 }
--> { 2, 5, 7, 13, 17, 19, 37 }
--> { 2, 5, 7, 13, 19, 23, 31 }
--> { 2, 5, 11, 13, 17, 23, 29 }
--> { 2, 5, 11, 17, 19, 23, 23 }
--> { 2, 7, 11, 13, 17, 19, 31 }
--> { 2, 3, 5, 7, 11, 13, 17, 19, 23 }

If anyone wants the source, I can share it here :D

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